Apply a volumetric texture tangentially on a torus
I was able to get a radial result:



The key is to use a 'Blend' type texture (instead of marble) as this has the option to do radial mapping:



I use a custom ramp for the black and white bars (set to 'constant' blending), a radial blend and default mapping settings.

One other setting which has to be enabled is 'RGB to intensity':



I use the default volume settings for the material, apart from 'Density' which is 0.